Homogeneous slip

It follows from this expression that the activation volume of a homogeneous slip may be as large as 2-3t)a. The activation volume of the slip-layer edge motion, as... 

A particular technique of mixture preparation is also used in the industry of traditional ceramics fdter-pressing. The various components (raw materials, dispersants, water) are mixed to form a fluid and homogenous slip. This slip is then filtered, under low pressure (0.5 MPa), through flexible filters ahgned on a frame to eliminate a large fraction of water and soluble species. The plastic paste obtained, with a small percentage of residual humidity, then exhibits a rheological behavior suitable for extrusion. 

Find the equilibrium, homogeneous specific volume v given by Eq, (26-85) and estimate the slip velocity ratio using the following correlation ... 

The first two eases represent the smallest and largest vent sizes required for a given rate at inereased pressure. Between these eases, there is a two-phase mixture of vapor and liquid. It is assumed that the mixture is homogeneous, that is, that no slip oeeurs between the vapor and liquid. Furthermore, the ratio of vapor to liquid determines whether the venting is eloser to the all vapor or all liquid ease. As most relief situations involve a liquid fraetion of over 80%, the idea of homogeneous venting is eloser to all liquid than all vapor. Table 12-3 shows the vent area for different flow regimes. 

The flow problems considered in previous chapters are concerned with homogeneous fluids, either single phases or suspensions of fine particles whose settling velocities are sufficiently low for the solids to be completely suspended in the fluid. Consideration is now given to the far more complex problem of the flow of multiphase systems in which the composition of the mixture may vary over the cross-section of the pipe or channel furthermore, the components may be moving at different velocities to give rise to the phenomenon of slip between the phases. 

Note that we have slipped in a height dependence of while still assuming homogeneity on smaller scales. 

Even in a homogeneous solid elastic wheel the distortion is complex and requires sophisticated methods to arrive at a precise relation between force and slip. For tires this is even more difficult because of its complex internal structure. Nevertheless, even the simplest possible model produces answers which are reasonably close to reality in describing the force-slip relation in measurable quantities. This model, called the brush model—or often also the Schallamach model [32] when it is associated with tire wear and abrasion—is based on the assumption that the wheel consists of a large, equally spaced number of identical, deformable elements (the fibers of a brush), following the linear deformation law... 

Any rheometric technique involves the simultaneous assessment of force, and deformation and/or rate as a function of temperature. Through the appropriate rheometrical equations, such basic measurements are converted into quantities of rheological interest, for instance, shear or extensional stress and rate in isothermal condition. The rheometrical equations are established by considering the test geometry and type of flow involved, with respect to several hypotheses dealing with the nature of the fluid and the boundary conditions the fluid is generally assumed to be homogeneous and incompressible, and ideal boundaries are considered, for instance, no wall slip. 

On the right are the t5rpes of point defects that could occur for the same sized atoms in the lattice. That is, given an array of atoms in a three dimensional lattice, only these two types of lattice point defects could occur where the size of the atoms are the same. The term vacancy is self-explanatory but self-interstitial means that one atom has slipped into a space between the rows of atoms (ions). In a lattice where the atoms are all of the same size, such behavior is energetically very difficult unless a severe disruption of the lattice occurs (usually a "line-defect" results. This behavior is quite common in certain types of homogeneous solids. In a like manner, if the metal-atom were to have become misplaced in the lattice cuid were to have occupied one of the interstitial... 

The homogeneous model treats the mixture as a whole, and consequently the physical properties are represented by the average value of the mixture. This treatment assumes that the gas and liquid phases possess the same velocity (or the slip velocity is neglected). This model was used extensively in the past, because of its simplic-... 

In reality, the slip velocity may not be neglected (except perhaps in a microgravity environment). A drift flux model has therefore been introduced (Zuber and Findlay, 1965) which is an improvement of the homogeneous model. In the drift flux model for one-dimensional two-phase flow, equations of continuity, momentum, and energy are written for the mixture (in three equations). In addition, another continuity equation for one phase is also written, usually for the gas phase. To allow a slip velocity to take place between the two phases, a drift velocity, uGJ, or a diffusion velocity, uGM (gas velocity relative to the velocity of center of mass), is defined as... 

Later, Weisman et al. (1978) also found that assuming homogeneous flow everywhere provided nearly as good a correlation of the data as the slip flow model. The total pressure drop across a contraction can be approximated by... 

In a homogeneous fluid the frictional resistance a particle experiences depends largely on its size and shape and on the nature of the solvent. For large molecules, where the slip factor (tendency of solvent molecules to adhere to solute) approaches infinity, the frictional resistance is... 

The homogeneous model also assumes that both phases are moving at the same velocity, i.e., no slip. Because the total mass flux is constant, the acceleration (or kinetic energy change) term can be written... 

For homogeneous equilibrium (no-slip) flow in a uniform pipe, the governing equation is [equivalent to Eq. (15-45)]... 

The presence of slip also means that the acceleration term in the general governing equation [Eq. (15-45)] cannot be evaluated in the same manner as the one for homogeneous flow conditions. When the acceleration term is expanded to account for the difference in phase velocities, the momentum equation, when solved for the total pressure gradient, becomes... 

The pressure drop over a given length of pipe must be determined by a stepwise procedure, as described for homogeneous flow. The major additional complication in this case is evaluation of the holdup (ipm) or the equivalent slip ratio (S) using one of the above correlations. 

H Homogeneous flow (slip velocity ratio of unity)... 

Sutherland (1975). Orifice flow rates are underpredicted by about the same factor with the energy balance method and with the NEM. Discharge predictions for short (0.2-m) pipes are overpredicted by the energy balance method. In this region, the assumption of homogeneous equilibrium is not justified. A model that takes slip velocity into account may improve predictions for short pipes. 

The definition of friction factor using mean fluid properties has been most widely used because it reduces to the correct single-phase value for both pure liquid and pure gas flow. This technique is very similar to the so-called homogeneous model, because it has a clear physical significance only if the gas and liquid have equal velocities, i.e., without slip. Variations of this approach have also been used, particularly the plotting of a ratio of a two-phase friction factor to a single-phase factor against other variables. This approach is then very similar to the Lockhart-Martinelli method, since it can be seen that (G4)... 

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